We present measurements of some of the principal response functions of a thin film of nanodimensional Fe particles embedded in A l2 O 3, specifically the temperature dependence of the moment measured under field cooled and zero field cooled conditions at temperatures between 5 K ≤ T ≤ 300 K in a low applied field ha =10 Oe , and the major hysteresis loop measured at T =5 K in applied fields between -2000 Oe ≤ h a ≤ + 2000 Oe . The data were analyzed within the framework of a generalized version of the Preisach model of hysteresis, which treats all magnetic systems as ensembles of interacting bistable Barkhausen elements, and which includes both thermal barrier relaxation effects and critical effects. Numerical simulations based on the model are able to replicate the principal structural features of the experimental data, and allow us to extract the characteristics of the bistable elements, specifically their moments μ, their coercive fields h c and their interaction fields h i .